In both of these cases, the "commercial" part of "commercial open source" is a reference to the add-on services and not the software licence itself. That said, it's important to read, understand, and ask questions about the licences for any products you use.

Without you saying just who they are I can't tell what license they are using. However it is possible for commercial and open source to go together. Open source means you can see the source code. They could make their money out of supporting the product, or maybe hosting it for you. That's the model that Red Hat use.